The product of two vectors can be done in two different ways. The result of one way
is another vector. The result of the other way is a scalar ... that's why that method
is called the "scalar product".
The way it's done is
(magnitude of one vector) times (magnitude of the other vector) times (cosine of the angle between them).
It depends on the type of product used. A dot or scalar product of two vectors will result in a scalar. A cross or vector product of two vectors will result in a vector.
Because there are two different ways of computing the product of two vectors, one of which yields a scalar quantity while the other yields a vector quantity.This isn't a "sometimes" thing: the dot product of two vectors is always scalar, while the cross product of two vectors is always a vector.
Scalar product = (magnitude of 'A') times (magnitude of 'B') times (cosine of the angle between 'A' and 'B')
The scalar product of two vectors, A and B, is a number, which is a * b * cos(alpha), where a = |A|; b = |B|; and alpha = the angle between A and B. The vector product of two vectors, A and B, is a vector, which is a * b * sin(alpha) *C, where C is unit vector orthogonal to both A and B and follows the right-hand rule (see the related link). ============================ The scalar AND vector product are the result of the multiplication of two vectors: AB = -A.B + AxB = -|AB|cos(AB) + |AB|sin(AB)UC where UC is the unit vector perpendicular to both A and B.
Dot Products in Physics denote scalar results fmo vector products, e.g Work = F.D = FDCos(FD) a scalar result from the dot product of two vectors, F Force and D Displacement.
It depends on the type of product used. A dot or scalar product of two vectors will result in a scalar. A cross or vector product of two vectors will result in a vector.
The product of scalar and vector quantity is scalar.
Torque is got by the cross product of two vectors namely force vector and perpendicular radius vector Tau (torque) = r X F But work is got by the scalar product of force vector and displacement vector Hence W = F . S
Work is the product of a force and a displacement. Both of those are vectors. There are two ways to multiply vectors. One of them produces another vector, the other produces a scalar. The calculation for 'work' uses the scalar product. The procedure is: (magnitude of one vector) times (magnitude of the other vector) times (cosine of the angle between them).
scalar, produced by the scalar product of two vector quantities ... Force · Distance
Work is the product of a force and a displacement. Both of those are vectors. There are two ways to multiply vectors. One of them produces another vector, the other produces a scalar. The calculation for 'work' uses the scalar product. The procedure is: (magnitude of one vector) times (magnitude of the other vector) times (cosine of the angle between them).
Because there are two different ways of computing the product of two vectors, one of which yields a scalar quantity while the other yields a vector quantity.This isn't a "sometimes" thing: the dot product of two vectors is always scalar, while the cross product of two vectors is always a vector.
Work is the product of a force a nd a displacement. Both of those are vectors. There are two ways to multiply vectors. One of them produces another vector, the other produces a scalar. The calculation for 'work' uses the scalar product. The procedure is: (magnitude of one vector) times (magnitude of the other vector) times (cosine of the angle between them). Answer2: Work is a scalar because Physics has a major defect in defining energy as a scalar. Nature defines energy as a Quaternion, the sum of a scalar and a vector. Work is a Quaternion, W = FD= -F.D + FxD , -F.D is a scalar and FxD is a vector. Physics defines Work as -FDcos(FD) and defines FxD = FDsin(FD) as Torque. When Physics understands Nature and Quaternions, then both F.D and FXD will both be recognized as energy, scalar energy and vector energy.
The scalar product of two perpendicular vectors is zero.In classical mechanics we define the scalar product between two vector a and b as:a · b = |a| |b| cos(alpha)where |a| is the modulus of vector a and alpha is the angle between vectors a and b.If two vectors are perpendicular, alpha equals 90º (or PI/2 rad) and cosine of alpha is, consequently, zero.So finally a · b = 0.
Power is the time derivative of energy, E. Energy can be scalar or vector. Thus power can be scalar or vector. Energy is a quaternion and consists of a scalar or real part Er and a vector part Ev. Energy E=Er + Ev, for example E= FR = -F.R + FxR = -FRCos(x) + FRsin(x). The real part is a scalar called "Energy" and the vector part is called "Torque" but has the same units Joules. Energy is defined by the units. P=dE/dt = d(Er + Ev)/dt = dEr/dt + dEv/dt = Pr + Pv. Power can be a scalar or a vector or both.
Scalar product = (magnitude of 'A') times (magnitude of 'B') times (cosine of the angle between 'A' and 'B')
Vector is NOT a scalar. The two (vector and scalar) are different things. A vector is a quantity (measurement) in which a direction is important. A scalar is a quantity in which a direction is NOT important.